Measure for Measure: Rhythm, Meter, and Tempo

In this installment, I'm taking a break from matters of tonality to slip in what I had originally thought of as my opening essay.

As my friend Graeme and I were driving to a Phillies game in April, he said "I know this sounds like a dumb question, but what is a measure in music?" If there's anything I've learned in life, it's that the dumb questions are always the ones most worth asking and are often the most difficult to answer. This one in particular turns out to be much more subtle and elusive than you might at first think.

Consider this passage from Johann Strauss Jr.'s waltz, "Tales of the Vienna Woods."

Example 1:

The music, I hope you'll agree, is carried by a clear, regular pulse - that is, it has a nice strong beat. If the music makes you tap your foot, or clap, or actually execute a Viennese waltz, you'll be hard put not to accent every third pulse. If you count the beat out loud, you'll naturally count "ONE-two-three, ONE-two-three."

Here's John Phillips Sousa's "El Capitán" March,

Example 2:

which, like any march, stresses every second pulse.

Even though it may seem too obvious to mention, it is crucial to note right at the outset that in both examples the duration of the beats is constant and therefore so is the time between the stressed beats. If we agree to call the stressed beats downbeats, then the answer to Graeme's question is:

A musical measure is the time that elapses between downbeats.

I think it's easy for most people to hear the downbeats and the way they are grouped in Examples 1 and 2; in the context of these examples, a measure seems like such a simple concept. Why is it then that the topic of musical time is so complicated and why does it generate so much incomprehensible prose?

First of all, if you have no formal musical training, you'll find it frustrating that many discussions of musical time are framed in terms of musical notation. But you don't need to read music, even a little bit, to understand Examples 1 and 2. A measure is simply a span of time.

If you learned to read music at an early age and have been striving to perform written music ever since, it can be hard to remember that musical notation is an attempt - and one that is never entirely successful - to express musical experience, not the other way around. There is no chicken-and-egg problem here. How do you think that Bach Prelude you're working on got onto the page in the first place?

Later in this section, I'll by necessity return to the relationship between what you hear and how it's written down, but for now, to quote a very wise musician friend of mine, this above all: The score is not the music!

The greatest source of trouble, though, is terminology.

As the title of the section indicates, there are three terms indispensable to any discussion of musical time: rhythm, meter and tempo.In many discussions of music, the terms rhythm and meter both create havoc, each in its own way, so, putting tempo aside for the moment, allow me to offer what I hope you'll find to be straightforward and useful definitions of these two problematic terms.

Rhythm: The patterns formed by sounds - and silence! - as time passes.

By this definition, if you can hear, the music never stops. That was the point of John Cage's notorious 1952 composition, 4' 33", in which a pianist sits at the keyboard for that amount of time and does nothing. Cage was trying to dramatize the fact that as soon as you put yourself in "I'm now listening to music mode", you don't perceive sound as you do when you're just going about the business of living; your mind tries to make musical "sense" (whatever that means) of what you are hearing. (Cage was, I believe, also making a joke at a time when the world of classical music was badly in need of some levity.)

Cage and many of his avant-garde cohorts were trying to redefine our culture's definition of music, but most people, then and now, persist in having very definite ideas about what "making musical sense" entails; there is a consensus that musical rhythm distinguishes itself from the random rhythms of ambient sound by creating a regular beat, by making us aware that time is passing by in discrete ticks or pulses.

The power of rhythmic patterns to create a sense of beat is so strong that the term "rhythm" is often used as a synonym for "sense of beat" (as in "I've Got Rhythm") and the word "arrhythmia" refers to a heartbeat that does not have a regular pulse. But I think it's important to be a stickler about this: Rhythm is not a synonym for regular beat; rhythm has the power to create beat.

Which brings us to my next definition:

Meter: The sensation of a regular pulse that arises from rhythm.

The term is intimately connected with the definition of measure: Example 1 illustrates triple meter; Example 2, duple meter. Another way of saying it is that Example 1 is "in three" while Example 2 is "in 2" .

I repeat: rhythm is not meter. The rhythms of these two examples happen to be strongly synchronized with the meters they create - they are strongly metrical rhythms - but, as we're about to see, a strong sense of meter can be created by a rhythmic pattern that depends as much on silence as it does on sound.

Before I demonstrate what I mean, though, we must deal with the confusion surrounding the term meter.

As we've already seen several times, musical terms are often ordinary English words used in ways that have nothing to do with their everyday meanings. Usually, the terms are so divorced from their usual sense - tonic and dominant from Section 4 are good examples - that we can just think of them as completely new words that coincidentally sound like more familiar ones.

The problem here is that meter also has a meaning with regard to poetry that seems at first to be related in some way to its musical one. It would have saved so much trouble if poetry and music didn't share the word - if, for example, tactus, the Renaissance term for musical meter, had survived as common usage today - because in fact poetic meter and musical meter really don't mean the same thing at all.

Poetic meter describes the ways accented and unaccented syllables are arranged in lines of poetry. On the surface, stresses in a poetic line might seem to be in some way the analog of the stresses of the beats in a measure. You can find many discussions of musical meter based on this premise; such discussions usually result in chaos. (As usual, one of the worst offenders is Wikipedia.)

In fact, since stressed and unstressed syllables are sometimes called "long" and "short", poetic meter seems to have more to do with rhythm than it does with musical meter. If you Google "poetic meter", you'll find many variations on "Meter is the rhythm of a poem.".

What a mess! Here's my attempt to clear it up.

In musical terms, if you're willing to accept my definitions above, poetic meter is neither rhythm nor meter - but when you put poetic meter into practice, you will find yourself forced to make musical decisions that create both.

Consider the beginning of Hamlet's famous soliloquy,

"To be or not to be: that is the question."

As you would expect, purely poetic analysis has a lot to tell us about how to read this line of iambic pentameter aloud.

The Wikipedia article on iambic pentameter uses many examples to illustrate the subtlety of the stress patterns of this poetic meter. And here's a link to an excellent discussion of the whole soliloquy that addresses, among many other things, the issue of whether one should say "... that is the question" or "...that is the question".

But such discussions never say anything specific about the duration of the syllables or phrases themselves or - and this is crucial - the duration of the silences between them.

How fast should you read the words? How much time should there be between "To be" and "or"? Between "be" and "that"? Should there be a little pause after "not"? Once you've made a decision about the stress of "that" vs. "is", what is the timing of "that is the"?

These are questions of musical rhythm; there are literally an infinite number of acceptable solutions, all of them true to the poetic meter but none of them dictated by it. Every time you read the line aloud, or hear it in your head, you must decide on your own. In short, whenever you make poetic meter manifest as recited poetry, you are composing music.

I urge you to take a shot at it yourself. Play with that line. Think about it. Read it aloud many times. I think you'll find that in the process of making rhythmic decisions about "To be or not to be..." you will find yourself counting to a regular beat - that is, your rhythmic decisions will generate a musical meter.

Here's what I came up with: 4 measures, each with 4 beats.

To be or not to be: That is the 1 2 3 4 1 2 3 4 1 2 3 4

question. 1 2 3 4

I wasn't really delighted with this solution; the timing of "That is" seems especially clunky to me. But I was just using Shakespeare's text to illustrate a point about rhythm and meter; I had no idea how an actual actor might deal with its rhythm. I was delighted by what I found when I began checking out the many YouTube clips of the soliloquy.

As you might expect, interpretations of this line are all over the map. Here's Mel Gibson's minimalist reading:

Example 3:

and here's Laurence Olivier's,

Example 4:

one of the few which accents the "is" of "that is the question."

But I wouldn't be going through all this were it not for Kevin Branagh and Derek Jacobi. Here's Branagh:

Example 5:

Before you listen to the next example, try to feel the underlying meter of Branagh's reading.

Now here is the same example with the beat made explicit.

Example 5a:

As any good musician would, Brahagh allows himself just a bit of flexibility in the beat, but, whether he is counting by design or instinct, his musical meter is strict.

For me, the real payoff is the silent downbeat before "that is the question"; it makes me want to stamp my foot or snap my fingers. And by distributing the syllables "that is the" evenly over the second beat (the musical terminology, by treating the syllables as a triplet), Branagh renders moot the argument about which syllable should be stressed by pushing all the weight onto "question".

Since my goal was to demonstrate how rhythm creates meter, for me the most important aspect of Example 5a is the silent measure at the end. Even after the words stop, the meter pulses on; for me, that last empty measure is as vital as the preceding three.

It's too bad that I had to cheat a bit to make this point. Branagh's version is a vast improvement on mine - well, duh! - but, if I were allowed to count that silent measure at the end, I could at least claim that it, like mine, still consists of four 4-beat measures. Alas, I must admit that in actuality, Branagh goes on to "Whether 'tis nobler in the mind..." before that fourth silent measure has run its course.

I don't know if Branagh and Derek Jacobi conferred about this line, but it sure sounds as if they did. Here's Jacobi speaking it

Example 6:

and here are Jacobi's and Branagh's versions played together.

Example 6a:

It's like two great pianists putting their individual stamps on a few measures from a Beethoven sonata.

To summarize:

The stress patterns of poetic meter combined with common sense suggest possibilities for musical rhythm but do not define them.

These rhythms have the potential to create a clear sense of regularly accented pulse - that is, musical meter.

For me, here is the most important aspect of musical meter: it is entirely a creation of the brain. The brain abstracts a sense of pulse from the rhythm of the pressure variations on the eardrum; one might even say that rhythm is real while meter is imaginary.

But then again, all our musical experience is imaginary in the same way. Our ability to create meter from rhythm is, perhaps even more than our ability to respond emotionally to pitch, the bedrock of human musical experience.

Of course, Examples 1 and 2, and indeed the remainder of the examples in this section, do not originate from speech, but that doesn't change the fact that musical rhythm is the parent of musical meter.

If you can hear where the measures are in Examples 1 and 2, you'll find, I think, that you'll also be able to find them in a great deal of the music you listen to. But not in all of it. Even if you feel that you understand what meter is conceptually, you will come across lots of music whose meters may well elude you. Here are some examples of what I mean, each one difficult in its own way.

An accent that occurs unexpectedly is called a syncopation. Syncopation occurs in myriad forms, but its effect depends on your knowing where the beat is supposed to be in the first place.

Here's one example from the third movement of Beethoven's Third Symphony, the "Eroica".

The movement is in an extremely fast triple meter, but Beethoven keeps on shifting the accent from every third beat to every second one. The example ends with one of the great syncopated moments in the symphonic literature.

Example 7:

While Beethoven's syncopations are typically jabs to the ribs, Mozart's are often just a little suggestive nudge under the table, like this passage from his last string quartet, K. 590.

Example 7a:

Now try this passage, the Sacrificial Dance from the end of Stravinsky's Rite of Spring.

Example 8:

Here, the beats are very strong, but they are grouped in such irregular and unpredictable patterns that Stravinsky himself said (somewhere) that he didn't know how to express them when he first heard them in his mind's ear. Example 8 could be said to be in a constant state of syncopation.

The rhythmic language of western European music - that is, of what we generically call classical music - is pretty tame when it is compared to the music of other cultures. Western ears, especially classically trained ones like mine, are used to hearing simple meters - that is, music whose meters are exclusively duple or triple.

For people like me, it takes some work to get accustomed to composite meters, in which, say, triple beats alternate with duple ones to form a measure of 7 beats. However, if your cultural roots are Balkan and/or if you've done a lot of international folk dancing, you are likely (I can only imagine) to feel perfectly at ease with this bit of Bulgarian folk music.

Example 9:

Here's the beat pattern, 3 + 2 + 2, played very slowly.

Example 9a:

When it's played faster, with beats 2, 5, and 7 silent, it becomes the rhythm of Example 9.

Here's an excerpt from Zyklus, a piece written by Karlheinz Stockhausen in 1959 for a percussion competition - one of my favorite pieces by one of my favorite composers.

Example 10:

The concept of measure is not applicable to Zyklus, which consists of little percussion events played in semi-randomly combined bunches. Stockhausen's directions say to play as many fragments as possible simultaneously and thus create as much silence - musical blank space - as possible.

But even in apparently simple cases, how do you ever know for sure where measures begin and end?

That is really an excellent question. For example, consider this, the beginning of Beethoven's Symphony No. 3, the "Eroica".

Example 11:

Are those two big chords at the beginning both downbeats? Should they be counted: "One! One!" or "One! Two!"?

If you pick the latter, it's pretty easy to hear the symphony moving along in a nice, easy duple meter. If you pick the former, though, then what is the meter? Unitary (One, One, One....)? Or can the time taken up by the first chord be reasonably broken down into faster beats?

How can you tell which is right? Similarly, how can you be sure what comprises a measure in Examples 1 and 2? In Example 1, couldn't you combine each pair of triple measures into a duple meter and, instead of counting "ONE-two-three, ONE-two-three", count "ONE-dum-dum, TWO-dum-dum"?

The truth is, as long as we can't ask Strauss or Beethoven what they intended, there is no way of knowing. Of course, we can ask them: Beethoven, Strauss, Mozart and all the rest left instructions about their intentions in the form of musical notation. In the case of the "Eroica", Beethoven told us that each of those two big chords chord is indeed a separate measure and that the music is in triple time. (It's so fast, though, that any sane conductor would only show the downbeats, conducting it as if there were only one beat to the measure.)

We need not concern ourselves with the rules for expressing music in written form. Suffice it to say that the notational system, in theory at least, allows a composer to communicate the two crucial pieces of information performers need about how a composition should organize time:

how many beats there are in a measure and

how fast those beats should go - that is, the music's tempo.

Tempo refers to the speed of the beat, not how fast the notes are going by. For example, in the following example, the beginning of the last movement of Mozart's 26th Piano Concerto, the rhythm gets increasingly more active but the tempo - that is the speed of the underlying beat - stays the same.

Example 12:

You'd think that defining a tempo would be a simple and precise matter: all you have to do is say, for example, "60 beats a minute." But it is clear from context that throughout the history of classical music, tempo has always been more a qualitative matter rather than a quantitative one.

For example, there are very few explicit tempo markings of any kind in either Book I or II of Johann Sebastian Bach's Well-Tempered Clavier - or in most of his music, for that matter. It's clear that he - and Baroque composers in general - thought that their music spoke for itself and left it up to the performer to choose a reasonable tempo, based on a combination of contemporary musical convention and common sense.

By the end of the 18th century, Haydn, Mozart, Beethoven et. al. were prefacing their scores with Italian adjectives like Allegro (fast), Presto (really fast!), Lento (slowly), etc. - what we today call tempo markings.

"Character marking" would be a more accurate term. If you Google "tempo marking", you'll find neatly ordered lists of all the commonly-used Italian words. But these lists simply do not reflect the subtleties of actual musical practice.

Take the words andante and allegretto.

Looking up andante in an Italian-English dictionary won't help very much; andante translates as "ordinary". From context, it's pretty clear that sometimes its musical meaning was something like "striding along with a strong sense of purpose," and sometimes something like "strolling along in a fairly leisurely fashion".

So what did Mozart mean when he marked the second movement of his 41st Symphony, the"Jupiter", "Andante Cantabile" - that is, a "singing andante"?

By today's performance standards, Norrington's reading sounds insanely fast to me; on the other hand, I wouldn't be astonished to learn, once my time-travel machine has been perfected, that Norrington comes closer to Mozart's intentions than Bernstein. (By the way, if you have no musical training and can count the slow triple meter of this passage without getting lost, you really should consider a career change. The rhythms of this movement are among the most complex and subtle ever conceived by the mind of man.)

And what about allegretto, which is simply the diminutive of allegro?

Allegretto is almost always defined as being a bit slower than allegro, but it's clear that to Mozart the difference was one of musical character, not tempo. Mozart's allegrettos are more playful, more from the world of comic opera, than his allegros, but they typically go like the wind as in Example Example 12, above.

On the other hand, andante and allegretto were almost the same tempo to Beethoven; he just couldn't make up his mind about them. Beethoven originally marked the second movement of his 7th Symphonyandante, but soon thereafter changed it to allegretto. (I'm perennially surprised to find that it's not marked andante.)

Example 14:

And then there's the incredible tempo marking of the opening of his Mass in C major. Clearly more concerned with feeling than precision, Beethoven directed the Mass to be played Andante con moto assai vivace quasi Allegretto ma non troppo - "Andante with motion, very lively, sort of like Allegretto, but not too much".

About 80 years later, Brahms seemed to be in the same sort of quandary about his B-flat minor Piano Intermezzo, Op. 117, No. 2, giving it this tempo marking: "Andante ma non troppo e con molto espressione", leaving it up to pianists like Radu Lupu to interpret what he meant.

Example 15:

And even though 20th century composers - Stravinsky, for example - tended more towards supplying exact tempos, many others, like Arnold Schoenberg, Anton Webern, and the wildly experimental American composer Charles Ives, still persisted in using descriptive tempo markings, perhaps with some loose guidelines about how fast the beat should go.

In short, although in theory there's nothing standing in the way of dictating musical tempos precisely, composers have for centuries steadfastly refused to do so. What does this imply about other aspects of music notation? Isn't the whole point of the system to enable the precise codification of a composer's musical intentions?

Precision! Aye, there's the rub!

Our culture's system for notating music excels at capturing complexity. Or, to put it another way, the elaborate musical structures that have been the hallmark of Western art music for the last thousand years or so could never have evolved without a notational system. But complexity is not the same as precision.

If you want to hear impeccably executed musical rhythms, listen to music like this,

Example 16:

vibraphonist Milt Jackson and the rest of the Modern Jazz Quartet in 1960 playing Duke Ellington's "It don't mean a thing (if it ain't got that swing)".

"That swing" - the subtle syncopation that makes jazz sound like jazz and enables a foxtrot to put a cushion of air under a dancer's feet - cannot be captured by musical notation. Similarly, Brahms had no way of expressing the nuances that Radu Lapu so eloquently brings to life in Example 15 other than to say "play with lots of expression". And if you listen carefully to Example 1 again, you'll hear that there is little bit of give and take in the triple meter, a flexibility of beat that, while it cannot be notated, is what makes a Viennese waltz sound like ... well, like a Viennese waltz!

Notated scores are full of symbols that try to capture the essence of what composers hear in their heads: "Accent here!", "Play sweetly", "Slow down", "Speed up ... even more!", "Stop counting for a bit", etc. These symbols can never entirely succeed because, taken all together, they are exhortations to be musical, to go beyond the literal - in short, to play the music as if it were poetry being read aloud, as if it were the expression of something very much akin to poetic meter.